I have a Purple Martin colony every year & have had to deal with a situation like this many times. Smaller chicks get pushed aside by the bigger chicks & end up starving. So I pull the larger ones for a few days hand feed them, then put them back. If you have to pull any I'd pull the largest one. Hand feed him a few days until the smallest one has a chance to catch up a bit. You'll need to place the pulled chick in a container with a lid/air holes & heating pad underneath. Set the heating pad on medium/low heat & place it under one end of the container. That way if he gets too warm he can move to a cooler spot. Keep him covered & away from bright light. You can use several layers of paper towels in the container, so it's easy to do clean up.
Good eggs should be white. Bad eggs will look off white or yellowish. However it's hard to tell since they've been laying in layers of poop. Good eggs will be heavier than bad eggs. Give them time to hatch & then toss those that are bad.
If you have access (neighbors, state park, etc) to the long soft pine needles that are dried (have turned brown & recently fallen off) they make a great soft nest & they do not absorb liquids. You can add a nice thick layer on top of the shavings.